Let X be a continuous random variable with PDF fX(x) = ( 2x for 0 < x

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Let X be a continuous random variable with PDF fX(x) =

(

2x for 0 < x < 1 , 0 otherwise.

a. Find E(X) and Var(X).

b. Suppose X1, X2, . . . , X40 are independent, each with the same distribution as X, and let Xsum = X1 + X2 + . . . + X40 .

What is the approximate distribution of Xsum?

c. What is the approximate distribution of the sample mean, X?

d. Specify an interval within which X will fall with roughly 95% probability.

e. Specify an interval within which X will fall with roughly 99.7% probability.

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Mathematics And Statistics For Science

ISBN: 9783031053177

1st Edition

Authors: James Sneyd, Rachel M. Fewster, Duncan McGillivray

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Question Posted: Sep 21, 2024 02:03 PM

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Let X be a continuous random variable with PDF fX(x) = ( 2x for 0 < x

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Mathematics And Statistics For Science

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